# Required Packages
import pandas as pd
import numpy as np
import pandas_datareader.data as pdr
from datetime import datetime, timedelta

# Visualisation libraries

## Text
from colorama import Fore, Back, Style
from IPython.display import Image, display, Markdown, Latex, clear_output

## progressbar
import progressbar

## plotly
from plotly.offline import init_notebook_mode, iplot 
import plotly.graph_objs as go
import plotly.offline as py
from plotly.subplots import make_subplots
import plotly.express as px

## seaborn
import seaborn as sns

## matplotlib
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse, Polygon
from matplotlib.font_manager import FontProperties
import matplotlib.dates as mdates
plt.style.use('seaborn-whitegrid')
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
plt.rcParams['text.color'] = 'k'
%matplotlib inline

## WordCloud
from wordcloud import WordCloud


import warnings
warnings.filterwarnings("ignore")

Home / Financial Analysis and Modeling

The Market Analysis

• The Market Analysis for Communication Services Sector
• The Market Analysis for Cryptocurrencies
• The Market Analysis for Technology Services

The Market Analysis for Communication Services Sector

In this article, the Communication Services Sector from Yahoo! Finance is used, and we analyze the current top tech companies' stock prices.

Table of contentens

• Stock Prices Fluctuations
• The Moving Average of the Stocks
• The Daily Return Average of a Stock
• The Correlation Between Daily Returns of Different Stocks
• Predicting Future Behaviors
  • Facebook, Inc.

Symbol	Name	Symbol	Name	Symbol	Name
GOOG	Alphabet Inc.	CHTR	Charter Communications, Inc.	BIDU	Baidu, Inc.
GOOGL	Alphabet Inc.	TMUS	T-Mobile US, Inc.	NTES	NetEase, Inc.
FB	Facebook, Inc.	VOD	Vodafone Group Plc	TEF	Telefonica, S.A.
T	AT&T Inc.	AMX	America Movil, S.A.B. de C.V.	CHA	China Telecom Corporation Limited
DIS	The Walt Disney Company	AMOV	America Movil, S.A.B. de C.V.	SIRI	Sirius XM Holdings Inc.
VZ	Verizon Communications Inc.	RELX	RELX PLC	EA	Electronic Arts Inc.
CMCSA	Comcast Corporation	BCE	BCE Inc.	CHT	Chunghwa Telecom Co., Ltd.
CHL	China Mobile Limited	ORAN	Orange S.A.
NFLX	Netflix, Inc.	ATVI	Activision Blizzard, Inc.

Symbols_list = ['GOOG','GOOGL','FB','T','DIS','VZ','CMCSA','NFLX','CHTR','TMUS','VOD','AMX','AMOV','RELX','BCE',
              'ORAN','ATVI','BIDU','NTES','TEF','CHA','SIRI','EA','CHT']

Symbols_Dic = {'GOOG':'Alphabet Inc.', 'GOOGL':'Alphabet Inc.', 'FB':'Facebook, Inc.','T':'AT&T Inc.',
            'DIS':'The Walt Disney Company','VZ':'Verizon Communications Inc.','CMCSA':'Comcast Corporation',
            'CHL':'China Mobile Limited','NFLX':'Netflix, Inc.','CHTR':'Charter Communications, Inc.',
            'TMUS':'T-Mobile US, Inc.','VOD':'Vodafone Group Plc','AMX':'America Movil, S.A.B. de C.V.',
            'AMOV':'America Movil, S.A.B. de C.V.','RELX':'RELX PLC','BCE':'BCE Inc.',
            'ORAN':'Orange S.A.','ATVI':'Activision Blizzard, Inc.','BIDU':'Baidu, Inc.',
            'NTES':'NetEase, Inc.','TEF':'Telefonica, S.A.','CHA':'China Telecom Corporation Limited',
            'SIRI':'Sirius XM Holdings Inc.','EA':'Electronic Arts Inc.','CHT':'Chunghwa Telecom Co., Ltd.'}

The data is collected from a years ago until now.

start, end = [datetime(datetime.today().year-5, 1, 1), datetime.today()]

def Timeline_plot(start, end, width = 16):
    fig, ax = plt.subplots(figsize=(width, 1))
    Temp = pd.date_range(start, datetime(end.year, end.month, 1), freq='MS')
    ax.plot((start, end), (0, 0), 'k', alpha=.5)
    ax.get_xaxis().set_major_locator(mdates.MonthLocator(interval=2))
    ax.get_xaxis().set_major_formatter(mdates.DateFormatter("%b %Y"))
    #fig.autofmt_xdate()
    _ = plt.setp((ax.get_yticklabels() + ax.get_yticklines() + list(ax.spines.values())), visible=False)
    for i in Temp:
        ax.scatter(i, 0, s=30, facecolor='#e74c3c', edgecolor='k')
    ax.grid(False)
    _  = plt.xticks(rotation=90)
    Temp1 = Temp.min().replace(day=1) - timedelta(days=1)
    Temp2 = Temp.max().replace(day=1) + timedelta(days=31)
    _ = ax.set_xlim ([datetime(Temp1.year,Temp1.month, 1), datetime(Temp2.year,Temp2.month, 1)]) 

Timeline_plot(start, end)

Collecting data from Yahoo Finance!, and creating moving Averages for 10, 20 and 60 day periods of time.

def Get_Data(Inp):
    Days = [10, 20, 60]
    Out = pdr.DataReader(Inp, 'yahoo', start, end)
    Out.insert(0, 'Symbol', Inp) 
    for j in Days:
        column_name = "Moving Ave. %s days" % (str(j))
        Out[column_name] = Out['Adj Close'].rolling(window=j, center=False).mean()
    return Out

Data = Get_Data(Symbols_list[0])

Counter = 0
Progress_Bar = progressbar.ProgressBar(maxval=len(Symbols_list),
                                       widgets=[progressbar.Bar('#', '|', '|'), progressbar.Percentage()])
Progress_Bar.start()
for i in Symbols_list[1:]:
    Counter+=1
    Progress_Bar.update(Counter)
    Temp = Get_Data(i)
    Data = pd.concat([Data, Temp])
    del Temp
Progress_Bar.finish()

Data [list(set(Data.columns)-{'Symbol'})] = Data[list(set(Data.columns)-{'Symbol'})].astype(float)

|#########################################################################|100%

Displaying today's data only:

Today = Data[Data.index == Data.index[-1]].reset_index(drop = True)
Today[list(set(Today.columns)-{'Symbol'})] = Today[list(set(Today.columns)-{'Symbol'})].astype(float)
Today['Symbol'] = Today['Symbol'].replace(Symbols_Dic)
display(Today.style.hide_index().set_precision(2).bar(subset=['Volume'], align='mid', color=['Lime'])\
        .bar(subset=['Adj Close'], align='mid', color=['Salmon'])\
        .set_properties(subset=['Symbol'], **{'background-color': 'Indigo', 'color': 'White'}))
print('Currently, the stock with the highest volume is %s' %
     Today.loc[Today.Volume == Today.Volume.max(),'Symbol'].values[0])

Symbol	High	Low	Open	Close	Volume	Adj Close	Moving Ave. 10 days	Moving Ave. 20 days	Moving Ave. 60 days
Alphabet Inc.	2277.14	2256.09	2261.47	2267.27	1059181.00	2267.27	2203.53	2128.54	2052.31
Alphabet Inc.	2263.47	2243.05	2250.99	2254.43	1215150.00	2254.43	2192.62	2117.41	2041.47
Facebook, Inc.	314.42	309.32	312.21	309.76	12422165.00	309.76	305.62	295.36	275.89
AT&T Inc.	29.86	29.51	29.86	29.63	39570988.00	29.63	30.06	29.82	28.96
The Walt Disney Company	186.44	184.60	185.59	185.49	6488604.00	185.49	187.20	188.44	185.90
Verizon Communications Inc.	57.76	57.16	57.37	57.62	15220334.00	57.62	57.85	57.07	55.87
Comcast Corporation	53.99	53.26	53.49	53.88	14639268.00	53.88	54.22	55.08	53.15
Netflix, Inc.	559.75	550.37	557.00	553.73	2653331.00	553.73	542.31	529.62	536.32
Charter Communications, Inc.	623.55	614.50	615.22	621.29	719170.00	621.29	615.88	627.01	622.51
T-Mobile US, Inc.	131.20	129.67	130.30	130.79	3028811.00	130.79	129.11	126.90	125.80
Vodafone Group Plc	18.68	18.47	18.50	18.64	2179223.00	18.64	18.73	18.76	18.27
America Movil, S.A.B. de C.V.	14.06	13.85	13.89	14.04	1223695.00	14.04	13.91	13.81	13.62
America Movil, S.A.B. de C.V.	14.30	14.03	14.19	14.23	1080.00	14.23	13.91	13.75	13.74
RELX PLC	26.49	26.24	26.29	26.47	338382.00	26.47	25.94	25.39	25.00
BCE Inc.	46.46	45.97	46.00	46.37	1056994.00	46.37	45.87	45.72	44.04
Orange S.A.	12.31	12.14	12.14	12.29	531858.00	12.29	12.43	12.45	12.07
Activision Blizzard, Inc.	98.25	96.51	97.00	97.54	5107020.00	97.54	95.92	93.80	94.98
Baidu, Inc.	217.37	207.69	209.60	216.56	8559513.00	216.56	220.35	232.72	261.08
NetEase, Inc.	107.21	103.68	103.82	106.21	1276616.00	106.21	104.88	105.36	113.11
Telefonica, S.A.	4.56	4.48	4.51	4.53	2196945.00	4.53	4.56	4.69	4.61
Sirius XM Holdings Inc.	6.24	6.16	6.24	6.20	15691466.00	6.20	6.25	6.23	6.12
Electronic Arts Inc.	143.88	141.51	142.59	142.11	1861271.00	142.11	139.82	135.45	138.63
Chunghwa Telecom Co., Ltd.	39.62	39.23	39.29	39.50	84205.00	39.50	39.36	39.16	39.23

Currently, the stock with the highest volume is AT&T Inc.

Consider AT&T Inc. for example. We hAve,

def Header(Text, L = 100, C = 'Blue', T = 'White'):
    BACK = {'Black': Back.BLACK, 'Red':Back.RED, 'Green':Back.GREEN, 'Yellow': Back.YELLOW, 'Blue': Back.BLUE,
         'Magenta':Back.MAGENTA, 'Cyan': Back.CYAN}
    FORE = {'Black': Fore.BLACK, 'Red':Fore.RED, 'Green':Fore.GREEN, 'Yellow':Fore.YELLOW, 'Blue':Fore.BLUE,
         'Magenta':Fore.MAGENTA, 'Cyan':Fore.CYAN, 'White': Fore.WHITE}
    print(BACK[C] + FORE[T] + Style.NORMAL + Text + Style.RESET_ALL + ' ' + FORE[C] +
          Style.NORMAL +  (L- len(Text) - 1)*'=' + Style.RESET_ALL)
    
def Line(L=100, C = 'Blue'):
    FORE = {'Black': Fore.BLACK, 'Red':Fore.RED, 'Green':Fore.GREEN, 'Yellow':Fore.YELLOW, 'Blue':Fore.BLUE,
         'Magenta':Fore.MAGENTA, 'Cyan':Fore.CYAN, 'White': Fore.WHITE}
    print(FORE[C] + Style.NORMAL + L*'=' + Style.RESET_ALL)
    
def Disp_Data(Inp, df = Data):
    Out = df[df.Symbol == Inp].drop(columns=['Symbol'])
    return Out

Temp = Disp_Data('T')
display(Temp.describe().round(2))

Tag = Temp.head(7).index[[0,-1]].astype(str).tolist()
Header('From %s To %s' % (Tag[0],Tag[1]))
display(Temp.head(7).dropna(axis = 1).round(2))


Tag = Temp.tail(7).index[[0,-1]].astype(str).tolist()
Header('From %s To %s' % (Tag[0],Tag[1]))
display(Temp.tail(7).round(2))

del Temp, Tag
Line()

	High	Low	Open	Close	Volume	Adj Close	Moving Ave. 10 days	Moving Ave. 20 days	Moving Ave. 60 days
count	1328.00	1328.00	1328.00	1328.00	1.328000e+03	1328.00	1319.00	1309.00	1269.00
mean	35.20	34.65	34.93	34.93	3.170162e+07	29.33	29.34	29.36	29.40
std	4.32	4.35	4.33	4.35	1.606388e+07	2.50	2.45	2.40	2.24
min	26.88	26.08	26.50	26.50	8.697200e+06	23.28	24.37	24.97	25.68
25%	31.01	30.40	30.72	30.70	2.160062e+07	27.50	27.51	27.55	27.67
50%	35.49	34.91	35.20	35.20	2.804705e+07	28.88	28.89	28.88	29.00
75%	38.73	38.22	38.50	38.50	3.755808e+07	30.79	30.67	30.63	30.69
max	43.89	43.33	43.50	43.47	1.950827e+08	35.83	35.54	35.28	34.96

From 2016-01-04 To 2016-01-12 ======================================================================

	High	Low	Open	Close	Volume	Adj Close
Date
2016-01-04	34.35	34.00	34.08	34.35	31779500.0	25.00
2016-01-05	34.69	34.12	34.35	34.59	30707300.0	25.18
2016-01-06	34.21	33.72	33.82	34.06	26911800.0	25.14
2016-01-07	34.10	33.51	33.62	33.51	35111400.0	24.74
2016-01-08	33.96	33.41	33.77	33.54	28090800.0	24.76
2016-01-11	34.10	33.53	33.76	33.95	26438800.0	25.06
2016-01-12	34.19	33.66	34.10	33.90	24124100.0	25.02

From 2021-04-05 To 2021-04-13 ======================================================================

	High	Low	Open	Close	Volume	Adj Close	Moving Ave. 10 days	Moving Ave. 20 days	Moving Ave. 60 days
Date
2021-04-05	30.84	30.60	30.62	30.71	38517300.0	30.19	29.80	29.59	28.80
2021-04-06	30.98	30.69	30.71	30.98	33666400.0	30.46	29.90	29.64	28.83
2021-04-07	31.15	30.80	31.01	30.93	40650500.0	30.41	29.99	29.70	28.86
2021-04-08	30.34	29.93	30.30	30.00	49877400.0	30.00	30.04	29.73	28.89
2021-04-09	30.19	29.91	30.05	30.04	33291800.0	30.04	30.09	29.78	28.92
2021-04-12	30.16	29.90	30.01	29.96	24830600.0	29.96	30.10	29.81	28.95
2021-04-13	29.86	29.51	29.86	29.63	39570988.0	29.63	30.06	29.82	28.96

====================================================================================================

Stock Prices Fluctuations

Temp = Data[['Symbol','Adj Close']].reset_index(drop = False)
Temp['Symbol'] = Temp['Symbol'].replace(Symbols_Dic)
fig = px.line(Temp, x='Date', y='Adj Close', color= 'Symbol')
fig.update_xaxes(rangeslider_visible=True, rangeslider =dict(bgcolor = 'WhiteSmoke'),
                 rangeselector=dict(bgcolor='WhiteSmoke', buttons=list([
                     dict(count=1, label='One Day', step='day', stepmode='todate'),
                     dict(count=1, label='One Month', step='month', stepmode='todate'),
                     dict(count=6, label='Six Months', step='month', stepmode='todate'),
                     dict(count=1, label='This Year', step='year', stepmode='todate'),dict(step='all')])))
fig.update_layout(plot_bgcolor= 'white')
fig.update_xaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                 showgrid=True, gridwidth=1, gridcolor='Lightgray')
fig.update_yaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                 showgrid=True, gridwidth=1, gridcolor='Lightgray')
fig.update_layout(title={'text': '<b>' + 'Stock Prices Fluctuations' + '<b>',
                         'x':.5, 'y': .98, 'xanchor': 'center', 'yanchor': 'top'})
fig.show()
del Temp

The following table shows the Average values for all columns of the Data.

def List_Search(List, Key): return [s for s in List if Key in s]

def List_Diff(Inp_A, Inp_B):
    # Inp_A: A list
    # Inp_B: A list
    Out=list(set(Inp_A)-set(Inp_B))
    return Out

# Creating a new list of Columns
Columns = List_Diff(Data.columns.tolist(), List_Search(Data.columns.tolist(), 'Moving Ave'))
Columns = List_Diff(Columns, ['Symbol'])
Temp = ['Ave. ' + i for i in Columns]

# A new DataFrame
Ave_df = pd.DataFrame({'Symbol':Symbols_list})
for i in Temp:
    Ave_df[i]=''
del Temp
# Progress Bar    
Counter = 0
Progress_Bar = progressbar.ProgressBar(maxval=len(Symbols_list),
                                       widgets=[progressbar.Bar('#', '|', '|'), progressbar.Percentage()])
Progress_Bar.start()
for i in range(len(Symbols_list)):
    Counter+=1
    Progress_Bar.update(Counter)
    Ave_df.iloc[i,1:] = Data[Data.Symbol == Symbols_list[i]][Columns].mean().values
               
Progress_Bar.finish()

display(Ave_df.style.hide_index().set_precision(2).bar(subset=['Ave. Volume'], align='mid', color=['Lime'])\
        .bar(subset=['Ave. Adj Close'], align='mid', color=['Salmon'])\
        .set_properties(subset=['Symbol'], **{'background-color': 'DimGray', 'color': 'White'}))

Temp = pd.melt(Ave_df, id_vars=['Symbol'], value_vars=list(set(Ave_df.columns)-{'Symbol'}),
               var_name='Summary', value_name='Value')

fig = make_subplots(rows=2, cols=1, vertical_spacing = 0.1, shared_yaxes=True,
                    subplot_titles=('Ave. Volume', 'Summary'))
# Top
fig1 = px.bar(Ave_df.round(0), x=  'Symbol', y= 'Ave. Volume', orientation='v', text = 'Ave. Volume',
              hover_data= Ave_df.columns)

for i in range(len(fig1['data'])):
    fig.add_trace(fig1['data'][i], row=1, col=1)
fig.update_traces(marker_line_color= 'Black', marker_line_width=1, opacity=1, row=1, col=1)

# Bottom
fig2 = px.bar(Temp.loc[Temp.Summary != 'Ave. Volume'].round(0), x=  'Symbol', y = 'Value',
              color = 'Summary', orientation='v', hover_data= Temp.columns)

for i in range(len(fig2['data'])):
    fig.add_trace(fig2['data'][i], row=2, col=1)
fig.update_traces(marker_line_color= 'Black', marker_line_width=1, opacity=1, showlegend = True, row=2, col=1)

# Update
fig.update_xaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                 zeroline=False, zerolinewidth=1, zerolinecolor='Black',
                 showgrid=True, gridwidth=1, gridcolor='Lightgray')
fig.update_yaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                 zeroline=False, zerolinewidth=1, zerolinecolor='Black', title_text='Value',
                 showgrid=False, gridwidth=1, gridcolor='Lightgray')
fig.update_layout(legend_orientation='v', plot_bgcolor= 'white', height= 800)
fig.update_layout(legend=dict(font=dict(color="Black"), bordercolor="Lightgray", borderwidth=1))

fig.update_layout(title={'text': '<b>' + 'Average Values' + '<b>', 'x':0.5, 'y': .95, 'xanchor': 'center', 'yanchor': 'top'})
fig.show() 

|#########################################################################|100%

Symbol	Ave. Volume	Ave. Adj Close	Ave. Low	Ave. Open	Ave. High	Ave. Close
GOOG	1666631.54	1138.07	1126.59	1137.15	1148.65	1138.07
GOOGL	1826994.01	1146.41	1134.71	1145.83	1157.21	1146.41
FB	21650941.77	177.60	175.44	177.53	179.60	177.60
T	31701622.58	29.33	34.65	34.93	35.20	34.93
DIS	9776028.54	115.15	116.47	117.61	118.64	117.58
VZ	15442835.42	47.93	53.25	53.67	54.07	53.68
CMCSA	20859867.14	37.03	38.55	38.95	39.34	38.96
NFLX	8900617.64	286.17	281.46	286.10	290.54	286.17
CHTR	1593585.37	380.32	375.76	380.08	384.71	380.32
TMUS	4227093.76	72.86	72.03	72.85	73.64	72.86
VOD	4328839.02	19.66	23.08	23.23	23.38	23.23
AMX	3080793.90	13.92	14.58	14.76	14.94	14.76
AMOV	7408.64	13.82	14.51	14.66	14.83	14.67
RELX	385190.88	20.49	21.49	21.60	21.72	21.61
BCE	948449.47	38.91	44.04	44.32	44.59	44.32
ORAN	476539.20	13.37	15.12	15.21	15.29	15.21
ATVI	7667649.26	58.33	58.22	59.05	59.80	59.05
BIDU	3945221.70	177.08	174.43	177.19	179.72	177.08
NTES	4857419.29	57.06	58.15	59.08	60.01	59.09
TEF	1645822.40	7.06	8.20	8.25	8.31	8.25
CHA	62818.44	40.96	44.82	45.10	45.33	45.07
SIRI	26985553.97	5.50	5.55	5.61	5.68	5.61
EA	3545828.22	104.36	103.24	104.63	105.88	104.61
CHT	149289.16	32.39	35.43	35.57	35.71	35.57

The Moving Average of the Stocks

def TopN_volumes(N, df = Ave_df):
    Out = df.sort_values(by='Ave. Volume', ascending=False).iloc[:N,0].tolist()
    return Out 

# Conisder the Moving Ave and Adj Close columns
Columns = List_Search(Data.columns.tolist(), 'Moving Ave.')
Columns.append("Adj Close")
Columns = list(np.sort(Columns))
# A list of top N = 4 companies with the hightest volume on Average.
N = 4
mylist = TopN_volumes(N)

# Conisder the Moving Ave and Adj Close columns
Columns = List_Search(Data.columns.tolist(), 'Moving Ave.')
Columns.append("Adj Close")
Columns = list(np.sort(Columns))
# A list of top N = 4 companies with the hightest volume on Average.
N = 4
mylist = Ave_df.sort_values(by='Ave. Volume', ascending=False).iloc[:N,0].tolist()

for symb in mylist:
    Temp = Disp_Data(symb)[Columns].reset_index(drop = False)
    Temp = pd.melt(Temp, id_vars=['Date'], value_vars= List_Diff(Temp.columns, ['Date']),
                   var_name='Variable', value_name='Value')

    fig = px.line(Temp, x='Date', y='Value', color = 'Variable')
    fig.update_xaxes(rangeslider_visible=True, rangeslider =dict(bgcolor = 'WhiteSmoke'),
                     rangeselector=dict(bgcolor='WhiteSmoke', buttons=list([
                         dict(count=1, label='One Day', step='day', stepmode='todate'),
                         dict(count=1, label='One Month', step='month', stepmode='todate'),
                         dict(count=6, label='Six Months', step='month', stepmode='todate'),
                         dict(count=1, label='This Year', step='year', stepmode='todate'),dict(step='all')])))
    fig.update_layout(plot_bgcolor= 'white')
    fig.update_xaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                     showgrid=True, gridwidth=1, gridcolor='Lightgray')
    fig.update_yaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                     showgrid=True, gridwidth=1, gridcolor='Lightgray')
    fig.update_layout(title={'text': '<b>' + Symbols_Dic[symb] + '<b>',
                             'x':.5, 'y': .97, 'xanchor': 'center', 'yanchor': 'top'})
    fig.show()
    del Temp
    
del symb

The Daily Return Average of a Stock

Daily return can be calculated using the percentage change of the adjusted closing price.

Daily_Return = Disp_Data(mylist[0])['Adj Close'].pct_change().to_frame('Daily Return').reset_index(drop = False)
Daily_Return['Symbols'] = mylist[0]
for stock in mylist[1:]:
    Temp = Disp_Data(stock)['Adj Close'].pct_change().to_frame('Daily Return').reset_index(drop = False)
    Temp['Symbols'] = stock
    Daily_Return = pd.concat([Daily_Return, Temp])
del Temp, stock
Daily_Return = Daily_Return.sort_values('Date')

fig = px.line(Daily_Return, x='Date', y='Daily Return', color = 'Symbols')
fig.update_xaxes(rangeslider_visible=True, rangeslider =dict(bgcolor = 'WhiteSmoke'),
                 rangeselector=dict(bgcolor='WhiteSmoke', buttons=list([
                     dict(count=1, label='One Day', step='day', stepmode='todate'),
                     dict(count=1, label='One Month', step='month', stepmode='todate'),
                     dict(count=6, label='Six Months', step='month', stepmode='todate'),
                     dict(count=1, label='This Year', step='year', stepmode='todate'),dict(step='all')])))
fig.update_layout(plot_bgcolor= 'white')
fig.update_xaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                 showgrid=True, gridwidth=1, gridcolor='Lightgray')
fig.update_yaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                 showgrid=True, gridwidth=1, gridcolor='Lightgray')
fig.update_layout(title={'text': '<b>' + 'Daily Returns' + '<b>',
                         'x':.5, 'y': .96, 'xanchor': 'center', 'yanchor': 'top'})
fig.show()
del Daily_Return

The Correlation Between Daily Returns of Different Stocks

First, we need to create a new data frame by reading the Adj Close column from all stock data under study. We hAve,

All_data = pdr.DataReader(Symbols_list, 'yahoo', start, end)['Adj Close']
All_returns = All_data.pct_change()

Tag = All_data.head(7).index[[0,-1]].astype(str).tolist()
Header('From %s To %s' % (Tag[0],Tag[1]), C = 'Black')
display(All_data.head(7).dropna(axis = 1).round(4))

Tag = All_data.tail(7).index[[0,-1]].astype(str).tolist()
Header('From %s To %s' % (Tag[0],Tag[1]), C = 'Black')
display(All_data.tail(7).dropna(axis = 1).round(4))

Line(C = 'Black')

From 2016-01-04 To 2016-01-12 ======================================================================

Symbols	GOOG	GOOGL	FB	T	DIS	VZ	CMCSA	NFLX	CHTR	TMUS	...	BCE	ORAN	ATVI	BIDU	NTES	TEF	CHA	SIRI	EA	CHT
Date
2016-01-04	741.84	759.44	102.22	25.0047	97.1558	35.9547	25.1296	109.96	177.53	38.95	...	29.9915	13.0994	36.3658	184.03	31.7791	8.0895	37.9867	3.8074	65.9303	23.9200
2016-01-05	742.58	761.53	102.73	25.1794	95.1934	36.4485	25.1342	107.66	175.17	40.22	...	30.2099	13.0285	35.9018	187.37	32.1004	8.0296	38.2234	3.7689	64.7733	23.9685
2016-01-06	743.62	759.33	102.97	25.1425	94.6840	36.1192	24.9400	117.68	174.31	40.05	...	30.3113	13.0994	35.5635	185.61	32.0653	7.9398	37.5471	3.7496	63.5165	23.9362
2016-01-07	726.39	741.00	97.92	24.7365	93.8726	35.9209	24.6645	114.56	173.63	40.51	...	29.7965	13.0915	35.0608	174.37	30.5329	7.9024	36.3550	3.7014	62.2996	23.8958
2016-01-08	714.47	730.91	97.33	24.7587	93.6367	35.5717	24.6916	111.39	174.89	39.88	...	29.8979	12.9812	34.5195	171.34	30.1802	7.7452	36.6255	3.6725	62.9679	24.0251
2016-01-11	716.03	733.07	97.51	25.0613	94.2688	35.7780	24.7141	114.97	175.63	39.68	...	29.9291	13.0127	35.0028	170.37	29.3180	7.7003	36.7354	3.6821	64.0451	24.5504
2016-01-12	726.07	745.34	99.37	25.0244	95.7217	35.6511	24.7819	116.58	175.32	40.06	...	30.4517	13.5014	35.8825	172.91	29.7002	7.7003	36.5917	3.6532	65.4515	24.6877

7 rows × 24 columns

From 2021-04-05 To 2021-04-13 ======================================================================

Symbols	GOOG	GOOGL	FB	T	DIS	VZ	CMCSA	NFLX	CHTR	TMUS	...	RELX	BCE	ORAN	ATVI	BIDU	NTES	TEF	SIRI	EA	CHT
Date
2021-04-05	2225.5500	2218.9600	308.91	30.1937	188.50	58.2434	54.550	540.67	605.50	131.40	...	26.03	45.86	12.57	97.87	222.29	105.54	4.60	6.30	141.54	39.51
2021-04-06	2224.7500	2209.2600	306.26	30.4592	189.73	58.4808	54.840	544.53	613.39	131.43	...	25.84	45.89	12.42	97.32	226.55	107.27	4.55	6.34	141.28	39.49
2021-04-07	2249.6799	2239.0300	313.09	30.4100	187.56	58.3720	54.600	546.99	611.63	130.02	...	26.03	45.93	12.49	96.84	222.00	103.39	4.59	6.33	142.01	39.61
2021-04-08	2265.4399	2250.4299	313.02	30.0000	187.32	57.6000	54.330	554.58	615.16	130.11	...	26.25	45.97	12.56	96.46	226.77	104.93	4.60	6.31	141.55	39.29
2021-04-09	2285.8799	2270.6699	312.46	30.0400	187.89	57.4900	53.570	555.31	614.24	129.03	...	26.43	46.22	12.50	95.78	219.67	103.94	4.57	6.35	140.46	39.40
2021-04-12	2254.7900	2244.6201	311.54	29.9600	186.49	57.5400	53.320	552.78	619.30	130.76	...	26.49	46.12	12.37	96.14	214.14	104.75	4.58	6.23	141.45	39.36
2021-04-13	2267.2700	2254.4299	309.76	29.6300	185.49	57.6200	53.875	553.73	621.29	130.79	...	26.47	46.37	12.29	97.54	216.56	106.21	4.53	6.20	142.11	39.50

7 rows × 23 columns

====================================================================================================

The returns can be analyzed using the percentage change from the adj Close.

Tag = All_data.tail(7).index[[0,-1]].astype(str).tolist()
Header('Returns (From %s To %s)' % (Tag[0],Tag[1]), C = 'Cyan', T = 'Black')
display(All_returns.tail(7).round(4))

Temp = pd.melt(All_returns.reset_index(drop = False), id_vars=['Date'],
               value_vars=list(set(All_returns.columns)-{'Date'}),
               var_name='Symbols', value_name='Daily Return')
Temp['Symbols'] = Temp['Symbols'].replace(Symbols_Dic)

fig = px.line(Temp, x='Date', y='Daily Return', color = 'Symbols')
fig.update_xaxes(rangeslider_visible=True, rangeslider =dict(bgcolor = 'WhiteSmoke'),
                 rangeselector=dict(bgcolor='WhiteSmoke', buttons=list([
                     dict(count=1, label='One Day', step='day', stepmode='todate'),
                     dict(count=7, label='One Week', step='day', stepmode='todate'),
                     dict(count=1, label='One Month', step='month', stepmode='todate'),
                     dict(count=6, label='Six Months', step='month', stepmode='todate'),
                     dict(count=1, label='This Year', step='year', stepmode='todate'),dict(step='all')])))
fig.update_layout(plot_bgcolor= 'white')
fig.update_xaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                 showgrid=True, gridwidth=1, gridcolor='Lightgray')
fig.update_yaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                 showgrid=True, gridwidth=1, gridcolor='Lightgray')
fig.update_layout(title={'text': '<b>' + 'Daily Returns' + '<b>',
                         'x':.5, 'y': .98, 'xanchor': 'center', 'yanchor': 'top'})
fig.show()

Returns (From 2021-04-05 To 2021-04-13) ============================================================

Symbols	GOOG	GOOGL	FB	T	DIS	VZ	CMCSA	NFLX	CHTR	TMUS	...	BCE	ORAN	ATVI	BIDU	NTES	TEF	CHA	SIRI	EA	CHT
Date
2021-04-05	0.0411	0.0419	0.0343	0.0079	-0.0025	0.0098	0.0009	0.0023	-0.0051	0.0294	...	0.0057	0.0170	0.0244	0.0118	-0.0099	0.0155	0.0	0.0048	0.0259	0.0097
2021-04-06	-0.0004	-0.0044	-0.0086	0.0088	0.0065	0.0041	0.0053	0.0071	0.0130	0.0002	...	0.0007	-0.0119	-0.0056	0.0192	0.0164	-0.0109	0.0	0.0063	-0.0018	-0.0005
2021-04-07	0.0112	0.0135	0.0223	-0.0016	-0.0114	-0.0019	-0.0044	0.0045	-0.0029	-0.0107	...	0.0009	0.0056	-0.0049	-0.0201	-0.0362	0.0088	0.0	-0.0016	0.0052	0.0030
2021-04-08	0.0070	0.0051	-0.0002	-0.0135	-0.0013	-0.0132	-0.0049	0.0139	0.0058	0.0007	...	0.0009	0.0056	-0.0039	0.0215	0.0149	0.0022	0.0	-0.0032	-0.0032	-0.0081
2021-04-09	0.0090	0.0090	-0.0018	0.0013	0.0030	-0.0019	-0.0140	0.0013	-0.0015	-0.0083	...	0.0054	-0.0048	-0.0070	-0.0313	-0.0094	-0.0065	0.0	0.0063	-0.0077	0.0028
2021-04-12	-0.0136	-0.0115	-0.0029	-0.0027	-0.0075	0.0009	-0.0047	-0.0046	0.0082	0.0134	...	-0.0022	-0.0104	0.0038	-0.0252	0.0078	0.0022	0.0	-0.0189	0.0070	-0.0010
2021-04-13	0.0055	0.0044	-0.0057	-0.0110	-0.0054	0.0014	0.0104	0.0017	0.0032	0.0002	...	0.0054	-0.0065	0.0146	0.0113	0.0139	-0.0109	0.0	-0.0048	0.0047	0.0036

7 rows × 24 columns

The following graphs show the correlation between different stocks.

_ = sns.jointplot('GOOG','GOOGL', All_returns, kind='reg', space=0, size=6, ratio=4)
_ = sns.jointplot('GOOGL','BIDU', All_returns, kind='reg', space=0, size=6, ratio=4)

Now, we can use the pairplot tool to visualize all.

# Remove missing values
Temp = TopN_volumes(8, df = Ave_df)
Temp = All_returns[Temp].dropna()
# plot
_ = sns.pairplot(Temp, diag_kind='kde')

Nonetheless, the correlation matrix and plot are always convenient to see numerical values for correlations.

# Correlation Matrix
Cor_matrix = Temp.corr()
display(Cor_matrix.style.set_caption('Correlation Matrix')\
    .background_gradient(cmap=sns.diverging_palette(5, 250, as_cmap=True)))

def Correlation_Plot (Df,Fig_Size):
    Correlation_Matrix = Df.corr()
    mask = np.zeros_like(Correlation_Matrix)
    mask[np.triu_indices_from(mask)] = True
    for i in range(len(mask)):
        mask[i,i]=0
    Fig, ax = plt.subplots(figsize=(Fig_Size,Fig_Size))
    sns.heatmap(Correlation_Matrix, ax=ax, mask=mask, annot=True, square=True, 
                cmap =sns.diverging_palette(5, 250, as_cmap=True), linewidths = 0.2, vmin=0, vmax=1, cbar_kws={"shrink": .5})
    bottom, top = ax.get_ylim()
    _ = ax.set_ylim(bottom + 0.5, top - 0.5)

Correlation_Plot (Temp, 10)

Correlation Matrix

Symbols	T	SIRI	FB	CMCSA	VZ	DIS	NFLX	ATVI
Symbols
T	1.000000	0.435569	0.244384	0.550447	0.660776	0.484567	0.144480	0.160600
SIRI	0.435569	1.000000	0.414805	0.489923	0.284895	0.428977	0.299586	0.293716
FB	0.244384	0.414805	1.000000	0.354370	0.201552	0.349036	0.469529	0.446290
CMCSA	0.550447	0.489923	0.354370	1.000000	0.449773	0.589540	0.276134	0.321856
VZ	0.660776	0.284895	0.201552	0.449773	1.000000	0.343187	0.118805	0.184146
DIS	0.484567	0.428977	0.349036	0.589540	0.343187	1.000000	0.227028	0.211305
NFLX	0.144480	0.299586	0.469529	0.276134	0.118805	0.227028	1.000000	0.454578
ATVI	0.160600	0.293716	0.446290	0.321856	0.184146	0.211305	0.454578	1.000000

Here, darker shades of blue represent a higher correlation.

Temp = All_returns.mean().to_frame('Expected Return').join(All_returns.std().to_frame('Risk')).reset_index(drop = False)
Temp['Symbols'] = Temp['Symbols'].replace(Symbols_Dic)

fig = px.scatter(Temp, x= 'Expected Return', y='Risk', color= 'Symbols', hover_data=Temp.columns)
fig.update_traces(marker_line_color= 'Black', marker_line_width=1, opacity=.5, showlegend = True)
# Update
fig.update_xaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                 zeroline=False, zerolinewidth=1, zerolinecolor='Black', range= [-0.001,0.002],
                 showgrid=True, gridwidth=1, gridcolor='Lightgray')
fig.update_yaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True, range= [0,0.03],
                 zeroline=False, zerolinewidth=1, zerolinecolor='Black', title_text='Value',
                 showgrid=True, gridwidth=1, gridcolor='Lightgray')
fig.update_layout(legend_orientation='v', plot_bgcolor= 'white', height= 500)
fig.show()

print("""The current trend seems to output a value between %.2e and %.2e.
We would like to identify a stock with high return and low risk!
""" % (Temp['Expected Return'].min(),Temp['Expected Return'].max()))

The current trend seems to output a value between -2.47e-04 and 1.55e-03.
We would like to identify a stock with high return and low risk!

We can find the quantile GOOG.

qt = All_returns['GOOG'].quantile(0.05)
qt_pct = abs(All_returns['GOOG'].quantile(0.05))*100
print('Quantile Percentage: %0.4f' % qt_pct)

print("""The 0.05 empirical quantile of daily returns is at {0:.2f}%.
      This means that with 95% confidence, the worst daily loss will not exceed {0:.2f}% (of the investment)."""
      .format(qt,qt_pct))

Quantile Percentage: 2.6156
The 0.05 empirical quantile of daily returns is at -0.03%.
      This means that with 95% confidence, the worst daily loss will not exceed -0.03% (of the investment).

Predicting Future Behaviors

To predict future behaviors, we can implement the Monte Carlo method (also see this [2] and this [3].

# consider a year
days = 365
# Delta t
dt = 1/365

Defining a Monte Carlo function fo the Stock price.

def stock_monte_carlo(start_price, days, mu, sigma):
    '''
    Function takes in stock price, number of days to run, mean and standard deviation values'''
    # An emptry array
    price = np.zeros(days)
    # Initial Price
    price[0] = start_price
    # Shock and drift
    shock = np.zeros(days)
    drift = np.zeros(days)
    
    # Formula: New price = Old price + Old price*(shock + drift)
    for x in range(1,days):       
        shock[x] = np.random.normal(loc=mu*dt,scale=sigma*np.sqrt(dt))        
        drift[x] = mu * dt
        price[x] = price[x-1] + (price[x-1] * (drift[x]+shock[x]))
    return price

def Monte_Carlo_Analysis(Inp, mu, sigma, N=1e2, days = days, Data = Data):
    # get the data for each symbol
    df = Data[Data.Symbol == Inp].drop(columns=['Symbol'])
    # set the last entry of the open column as the starting price
    start_price = df['Open'][-1]
    # Ouput Figure
    N = int(N)
    fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize=(16, 8))
    for run in range(100):
        _ = plt.plot(stock_monte_carlo(start_price, days, mu, sigma))
        _ = ax.set_xlabel('Days')
        _ = ax.set_ylabel('Price')
        _ = ax.set_title('Monte Carlo Analysis for %s' % Symbols_Dic[Inp], weight='bold', fontsize = 16)
    _ = ax.set_xlim([0,days])
    return df

def Final_price_distribution_simulations(Inp, mu, sigma, N= 1e4, days = days, Data = Data):
    # get the data for each symbol
    df = Data[Data.Symbol == Inp].drop(columns=['Symbol'])
    # set the last entry of the open column as the starting price
    start_price = df['Open'][-1]
    # Simulations array
    N = int(N)
    simulations = np.zeros(N)
    # Progress Bar    
    Counter = 0
    Progress_Bar = progressbar.ProgressBar(maxval= N, widgets=[progressbar.Bar('#', '|', '|'), progressbar.Percentage()])
    Progress_Bar.start()
    for i in range(N):
        simulations[i] = stock_monte_carlo(start_price, days, mu, sigma)[days-1]
        Counter+=1
        Progress_Bar.update(Counter)
    Progress_Bar.finish()
    return simulations

def Final_price_distribution_plot(simulations, Inp, Data = Data):
    # get the data for Inp teach
    df = Data[Data.Symbol == Inp].drop(columns=['Symbol'])
    # set the last entry of the open column as the starting price
    start_price = df['Open'][-1]
    # Output Figure
    fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize=(16, 8))
    q = np.percentile(simulations, 1)
    _ = ax.hist(simulations, bins='auto', color = '#34495e')
    _ = plt.figtext(0.75, 0.80, "Start price: $%.2f" % start_price, fontsize = 12)
    _ = plt.figtext(0.75, 0.75, "Mean final price: $%.2f" % simulations.mean(), fontsize = 12)
    _ = plt.figtext(0.75, 0.70, "VaR(0.99): $%.2f" % (start_price -q,), fontsize = 12)
    _ = plt.figtext(0.15,0.665, "q(0.99): $%.2f" % q, fontsize = 12)
    _ = ax.set_xlim()
    _ = ax.axvline(x=q, linewidth=4, color='#e74c3c')
    _ = ax.set_title("Final price distribution for %s after %s days" % (Symbols_Dic[Inp], days), weight='bold', fontsize = 16)

Facebook, Inc.

Symbol = 'FB'
# mean
mu = All_returns.mean()[Symbol]
# standard deviation
sigma = All_returns.std()[Symbol]
_ = Monte_Carlo_Analysis(Symbol, mu = mu, sigma = sigma)

The frequencies of different outcomes simulated form a Bell curve. The most likely return is in the middle of the curve. This means there is an equal chance that the actual return will be higher or lower than that value.

Simulations = Final_price_distribution_simulations(Symbol,  mu = mu, sigma = sigma)
Final_price_distribution_plot(Simulations, Symbol)

|#########################################################################|100%

See more details about Value at Risk (VaR) [4].

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References

1. Yahoo Finance
2. Mathematical Foundations of Monte Carlo Methods
3. Monte Carlo Simulation
4. An Introduction to Value at Risk (VAR)
5. Bell Curve

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